Related papers: On a Problem of Bremermann Concerning Runge Domain…

On a bounded strictly pseudoconvex domain in $\mathbb{C}^n$, $n>1$, the smoothness of the Cheng-Yau solution to Fefferman's complex Monge-Ampere equation up to the boundary is obstructed by a local CR invariant of the boundary. For a…

In this paper, we show that a compact real surface embedded in a complex surface has a regular Stein neighborhood basis, provided that there are only finitely many complex points on the surface, and that they are all flat and hyperbolic. An…

Let $k$ be a non-archimedean complete valued field and $X$ be a $k$-analytic space in the sense of Berkovich. In this note, we prove the equivalence between three properties: 1) for every complete valued extension $k'$ of $k$, every…

It is shown that the unit ball in ${\mathbb C}^n$ is the only complex manifold that can universally cover both Stein and non-Stein strictly pseudoconvex domains.

We describe recent work on the Bergman kernel of the (non-smooth) worm domain in several complex variables. An asymptotic expansion is obtained for the Bergman kernel. Mapping properties of the Bergman projection are studied. Irregularity…

We generalize to intersection of strictly $c$ -convex domains in Stein manifold, $ L^{r}-L^{s}$ and Lipschitz estimates for the solutions of the $ \bar \partial $ equation done by Ma and Vassiliadou for domains in $ {\mathbb{C}}^{n}.$ For…

With the aid of the technique of variation of domains developed in Memoirs of Amer. Math. Soc., Vol. 209, No. 984, 2011, we characterize the pseudoconvex domains with smooth boundary in Hopf surfaces which are not Stein.

Domains that are increasing union of balls (up to biholomorphism) and on which the Kobayashi metric vanishes identically arise inexorably in complex analysis. In this article we show that in higher dimensions these domains have infinite…

On a bounded strictly pseudoconvex domain in $\mathbb{C}^n$, $n>1$, the smoothness of the Cheng-Yau solution to Fefferman's complex Monge-Ampere equation up to the boundary is obstructed by a local curvature invariant of the boundary. For…

We introduce the notion of domains with uniform squeezing property, study various analytic and geometric properties of such domains and show that they cover many interesting examples, including Teichmuller spaces and Hermitian symmetric…

This paper is concerned with a Neumann type problem for singularly perturbed fractional nonlinear Schr\"odinger equations with subcritical exponent. For some smooth bounded domain $\Omega\subset \mathbf R^n$, our boundary condition is given…

In recent work by Zimmer it was proved that if $\Omega\subset\mathbb C^n$ is a bounded convex domain with $C^\infty$-smooth boundary, then $\Omega$ is strictly pseudoconvex provided that the squeezing function approaches one as one…

Let D be a smoothly bounded domain in complex space of dimension larger than 2. Suppose that D admits a smooth defining function which is plurisubharmonic on the boundary of D. Then the Diederich-Fornaess exponent can be chosen arbitrarily…

We study the Diederich-Forn{\ae}ss exponent and relate it to non-existence of Stein domains with Levi-flat boundaries in complex manifolds. In particular, we prove that if the Diederich-Forn{\ae}ss exponent of a smooth bounded Stein domain…

We study the strong solvability of the nonstationary Stokes problem with non-zero divergence in a bounded domain.

In this paper, we construct unbounded domains in $\C^n$ ($n\geq 2$), whose Bergman spaces are nontrivial and finite-dimensional. We further show that the Bergman metrics on these domains have positive constant sectional curvature equal to…

It is shown that two strictly pseudoconvex Stein domains with real analytic boundaries have biholomorphic universal coverings provided that their boundaries are locally biholomorphically equivalent. This statement can be regarded as a…

Given a domain Y in a complex manifold X, it is a difficult problem with no general solution to determine whether Y has a schlicht envelope of holomorphy in X, and if it does, to describe the envelope. The purpose of this paper is to tackle…

We prove that all locally exposable points in a Stein compact in a complex space can be exposed along a given curve to a given real hypersurface. Moreover, the exposing map for a boundary point can be sufficiently close to the identity map…

Let $D$ be a bounded domain in $\mathbf C^2$ with a non-compact group of holomorphic automorphisms. Model domains for $D$ are obtained under the hypothesis that at least one orbit accumulates at a boundary point near which the boundary is…